CBEMS155-W12-Set#2(a) - 3 For a particular stress tensor σ...

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University of California, Irvine Chemical Engineering and Materials Science Mechanical and Aerospace Engineering CBEMS155/MAE156 FAM Winter 2012 Due: Monday, February 6 th (by 3:00 p.m.) Problem Set 2(a) 1. Using the knowledge of vectors and algebra, derive the following equations: (Outcome #1) a. σ zr = σ zz l zr + τ zx l xr + τ zy l yr b. σ nx = τ yx l yn + σ xx l xn + τ zx l zn (where n is the normal to the plane) 2. The components of a stress tensor at a point for a system of reference axes x, y, z are given by: 0 0 300 0 -400 0 MPa 300 0 -800 Using the knowledge of algebra, determine the following ( Outcome #1 ) a. Determine the values of the principal normal stresses (use two procedures). (Ans: 100 MPa, -400 MPa, -900 MPa) b. Determine the values of principal shear stresses. (Ans: 250 MPa, 250 MPa, 500 MPa) c. Show by calculation that the invariants are independent of the reference axes.
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Unformatted text preview: 3. For a particular stress tensor σ x = 9 MPa, σ y = 20 MPa and σ z = -20 MPa. If σ 1 = 3 and σ 2 = 2, what is the value of σ 3 ? ( σ 1 , σ 2, and σ 3 are principal normal stresses). (Ans: 4 MPa) 4. Explain why : (a) Studying stress analysis under the condition of 3-D is important. (b) Charpy impact test is a simple test for studying energy absorbed before facture. (c) The use of notched specimen in the charpy test. (d) Ductility is important (e) Knowledge about anisotropy is important 5. What is the difference between? (a) Strength and stress, (b) Tensor of the first rank and tensor of the second rank, (c) The proportional limit and the elastic limit, (d) the stress strain curve for a metal and that of a polymer, (e) Tensile strain and shear strain 2...
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This note was uploaded on 02/20/2012 for the course CBEMS 45B taught by Professor Shi during the Spring '12 term at UC Irvine.

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CBEMS155-W12-Set#2(a) - 3 For a particular stress tensor σ...

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